Hausdorff core of a one reflex vertex polygon

In this paper we present a polynomial time algorithm for computing a Hausdorff core of a polygon with a single reflex vertex. A Hausdorff core of a polygon P is a convex polygon Q contained inside P which minimizes the Hausdorff distance between P and Q. Our algorithm essentially consists of rotating a line about the reflex vertex; this line defines a convex polygon by cutting P. To determine the angle at which the line should be rotated, our algorithm searches for a global minimum on the upper envelope of n continuous piecewise functions, where n is the number of vertices of P.

• Type: Conference
• Year: 2010
• Where: CCCG
• Authors: Robert Fraser, Patrick K. Nicholson
• Keywords: CCCG 2010, Computational Geometry, Convex Polygon, Hausdorff Core, Reflex Vertex